We study the m = 3 bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability p or 1 − p, respectively. Occupied sites with less than m occupied first-neighbours are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, pc, and both scaling powers, yp and y h , and, contrarily to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., m = 0). The critical spanning probability, R(pc), is also numerically studied, for systems with linear sizes ranging from L = 32 up to L = 480: the value we found, R(pc) = 0.270 ± 0.005, is the same as for usual percolation with free boundary conditions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.